A minimax approach to mapping partial interval uncertainties into point estimates

• Autorzy: Romanuke Vadim

Identyfikatory

DOI

10.7862/rf.2019.10

• Języki publikacji: EN

Abstrakty

EN

A problem of simultaneously reducing a group of interval uncertainties is considered. The intervals are positively normalized. There is a constraint, by which the sum of any point estimates taken from those intervals is equal to 1. Hence, the last interval is suspended. For mapping the interval uncertainties into point estimates, a minimax decision-making method is suggested. The last interval’s point estimate is then tacitly found. Minimax is applied to a maximal disbalance between a real unknown amount and a guessed amount. These amounts are interpreted as aftermaths of the point estimation. According to this model, the decision-maker is granted a pure strategy, whose components are the most appropriate point estimates. Such strategy is always single. Its components are always less than the right endpoints. The best mapping case is when we obtain a totally regular strategy whose components are greater than the left endpoints. The irregular strategy’s components admitting many left endpoints are computed by special formulae. The worst strategy exists, whose single component is greater than the corresponding left endpoint. Apart from the point estimation, irregularities in the decision-maker’s optimal strategy may serve as an evidence of the intervals’ incorrectness. The irregularity of higher ranks is a criterion for correcting the intervals.

Słowa kluczowe

EN

game theory; interval uncertainties; decision-making; pure strategy; point estimates

PL

teoria grup; niepewności przedziałowe; podejmowanie decyzji; strategia czysta; oszacowania punktowe

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2019
• Tom: Vol. 42
• Strony: 147--185
• Opis fizyczny: Bibliogr. 51 poz., rys., wykr.

Twórcy

autor

Romanuke Vadim

• Faculty of Navigation and Naval Weapons, Polish Naval Academy, Gdynia, POLAND

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).